A right triangle has 20 inches long hypotenuse. Prove that the triangle is an isosceles triangle with maximum perimeter

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maximum-perimeter

#1

A right triangle has 20 inches long hypotenuse. Prove that the triangle is an isosceles triangle with maximum perimeter

Answer:

In a simple example, leg 1 and leg 2 are set congruent at a side length of 1 and their base angles are 45 degrees each. The hypotenuse can be calculated using the Pythagorean Theorem because 1^2+1^2=c^2 (c is hypotenuse) will give you what you need to start with. 1^2=1, so both a and b are solved in 1 step. 1+1=2=c^2. Solve by finding the square root of 2. The square root of 2 is the answer for the length of the hypotenuse.

Now, reverse engineer the question. Set up a proportion. (Square root of 2)/1=20/x

Cross-multiply 1x20 to get 20 and divide by the 2. The answer isn’t pretty, but one leg length is 14.14213562 (rounded off to 10 significant digits). Add the 20, 14.14 (approx.) and 14.14 to get a perimeter of 48.28427124 and maybe round if your teacher wants that.

Anyway, Perimeter=48.28427124 u